EJMT Abstract

We explore with technological tools on some problems that originated from a college practice entrance question (see [12]). The problems involve an affine transformation whose image is a locus based on lines passing through a fixed point (see Figure 1(a) or 1(b)), which has been explored in ([17], [18], [19], [20]) by using parametric equations. We are interested in the topological structures for the shapes of image curves or surfaces when the scaling factor s vary. We found the value for s which affects the topological structures for the loci in 2D first, and we extend the results to 3D based on the arguments in 2D. Finally, we include an exploration on the topological structure for the locus ellipsoid when scaling factor s and the fixed point A approach to infinity.